First, what model modem/router/gateway do you have? I think Cox only supports their Panoramic gateway that they rent so if they suspect a hardware issue, they pass the buck to the manufacture. I think they will support retail modems if you sign up for Cox Complete Care however we(the forum) might be able to help isolate the issue. Start by posting your modem's signal levels. Also look at your event logs at the time of the disconnects. I bet it is a T3 time out issue from noise, usually cellular ingress, on the upstream. I can give instructions once I know what equipment you have.